Consider the quadratic function f(x) in the form f(x) = xQx-xb, where Q = Rmxn is a symmetric positive definite matrix, b = R", and x = R". (a) (10 marks) Show that the gradient of f(x) is Vf(x)=Qx-b. (b) (5 marks) Show that the Hessian of f(x) is F = Q. (c) (5 marks) Write down the formula for Newton's iteration method (that is, how to find x(+1) in terms of x()) for finding the minimum of f(x). (d) (10 marks) Show that for a quadratic function f(x), Newton's method reaches the extremiser x* in just one step starting from any initial point x(0).